Subgame

Definition

A subgame is a portion of an extensive form game that begins at a decision node and includes all subsequent decisions and outcomes from that point onward. Subgames can be thought of as smaller games within the larger game, where players make decisions based on the information and strategies available at that specific stage. The concept of subgames is crucial for analyzing strategies and determining equilibrium points within extensive form games.

5 Must Know Facts For Your Next Test

1. Subgames can exist at any point in the extensive form game, provided there are future decisions and outcomes from that point forward.
2. In order to analyze a subgame, it must be self-contained, meaning all necessary information for decision-making must be present within the subgame itself.
3. The concept of subgames is essential for applying backward induction, where players anticipate future decisions and outcomes to determine optimal strategies.
4. A strategy profile can be evaluated based on its performance in each subgame to ensure that it is optimal across the entire extensive form game.
5. Subgame perfect equilibrium is a refinement of Nash equilibrium used specifically in extensive form games, requiring that strategies constitute a Nash equilibrium in every subgame.

Review Questions

• How does identifying subgames within an extensive form game help players strategize more effectively?
  • Identifying subgames allows players to focus on specific segments of the game where they can make strategic decisions based on the available information at that stage. This breakdown simplifies complex decision-making processes, enabling players to consider how their current choices will influence future outcomes and other players' responses. By analyzing each subgame independently, players can refine their overall strategy to achieve better results in the complete game.
• Discuss the importance of subgame perfect equilibrium in extensive form games and how it differs from standard Nash equilibrium.
  • Subgame perfect equilibrium is vital because it ensures that players' strategies remain optimal not just in the entire game but also in every possible subgame. This distinction is important because standard Nash equilibrium may allow for non-credible threats or actions that aren't sustainable when considering future decisions. In contrast, subgame perfect equilibrium requires that players choose strategies that would still be rational and optimal even if they find themselves at different stages of the game.
• Evaluate the role of backward induction in analyzing subgames and how it leads to finding optimal strategies in extensive form games.
  • Backward induction plays a crucial role in analyzing subgames by allowing players to reason backwards from the game's end to determine optimal strategies at earlier stages. By starting at the final decision points within each subgame and working backwards, players can predict how others will react and what choices will maximize their own payoffs. This method ensures that strategies align with the dynamics of every possible subgame, leading to a comprehensive understanding of optimal play throughout the extensive form game.

Related terms

Extensive Form Game: A representation of a game that depicts players, their available strategies, and the sequential nature of their choices using a tree structure.

Nash Equilibrium: A situation in a game where no player can benefit by changing their strategy while the other players keep theirs unchanged.

Perfect Information:

A situation in a game where all players are fully aware of all previous actions taken, allowing them to make informed decisions.